Question
Euclid Elementary School is graphed at (−4, 1), Math Middle School is graphed at (1, 1), and Hypotenuse High School is graphed at (−4, −3). Each unit on the graph represents 1 mile.
Part A: Find the shortest distance, in miles, from Euclid Elementary School to Math Middle School. Show every step of your work.
Part B: Find the shortest distance, in miles, from Euclid Elementary School to Hypotenuse High School. Show every step of your work.
Part C: Find the shortest distance, in miles, from Math Middle School to Hypotenuse High School. Show every step of your work.
Part D: Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. Kaya traveled from Hypotenuse High to Math Middle along a straight path. Who went the shortest distance? Explain.
Part A: Find the shortest distance, in miles, from Euclid Elementary School to Math Middle School. Show every step of your work.
Part B: Find the shortest distance, in miles, from Euclid Elementary School to Hypotenuse High School. Show every step of your work.
Part C: Find the shortest distance, in miles, from Math Middle School to Hypotenuse High School. Show every step of your work.
Part D: Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. Kaya traveled from Hypotenuse High to Math Middle along a straight path. Who went the shortest distance? Explain.
Answers
Answer
bot could you repeat everything you just said but take out sqrt
Answer
repeat everything you just said but take out the checkmarks and don't add sqrt
Answer
are you sure this is right?
Answered by
GPT 3.5
To find the shortest distance between two points in the coordinate plane, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Part A: Finding the shortest distance from Euclid Elementary School to Math Middle School.
Coordinates of Euclid Elementary School: (-4, 1)
Coordinates of Math Middle School: (1, 1)
Distance = sqrt((1 - (-4))^2 + (1 - 1)^2)
= sqrt(5^2 + 0^2)
= sqrt(25)
= 5 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 5 miles.
Part B: Finding the shortest distance from Euclid Elementary School to Hypotenuse High School.
Coordinates of Euclid Elementary School: (-4, 1)
Coordinates of Hypotenuse High School: (-4, -3)
Distance = sqrt((-3 - 1)^2 + (-4 - (-4))^2)
= sqrt((-4)^2 + 0^2)
= sqrt(16)
= 4 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 4 miles.
Part C: Finding the shortest distance from Math Middle School to Hypotenuse High School.
Coordinates of Math Middle School: (1, 1)
Coordinates of Hypotenuse High School: (-4, -3)
Distance = sqrt((-3 - 1)^2 + (-4 - 1)^2)
= sqrt((-4)^2 + (-5)^2)
= sqrt(16 + 25)
= sqrt(41)
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is sqrt(41) miles.
Part D: Comparing the distances traveled by Deon and Kaya.
Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle.
Kaya traveled from Hypotenuse High to Math Middle along a straight path.
We can compare the distances:
Deon's distance = 4 + 5 = 9 miles
Kaya's distance = sqrt(41) miles
Therefore, Kaya traveled the shortest distance because sqrt(41) is less than 9.
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Part A: Finding the shortest distance from Euclid Elementary School to Math Middle School.
Coordinates of Euclid Elementary School: (-4, 1)
Coordinates of Math Middle School: (1, 1)
Distance = sqrt((1 - (-4))^2 + (1 - 1)^2)
= sqrt(5^2 + 0^2)
= sqrt(25)
= 5 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 5 miles.
Part B: Finding the shortest distance from Euclid Elementary School to Hypotenuse High School.
Coordinates of Euclid Elementary School: (-4, 1)
Coordinates of Hypotenuse High School: (-4, -3)
Distance = sqrt((-3 - 1)^2 + (-4 - (-4))^2)
= sqrt((-4)^2 + 0^2)
= sqrt(16)
= 4 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 4 miles.
Part C: Finding the shortest distance from Math Middle School to Hypotenuse High School.
Coordinates of Math Middle School: (1, 1)
Coordinates of Hypotenuse High School: (-4, -3)
Distance = sqrt((-3 - 1)^2 + (-4 - 1)^2)
= sqrt((-4)^2 + (-5)^2)
= sqrt(16 + 25)
= sqrt(41)
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is sqrt(41) miles.
Part D: Comparing the distances traveled by Deon and Kaya.
Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle.
Kaya traveled from Hypotenuse High to Math Middle along a straight path.
We can compare the distances:
Deon's distance = 4 + 5 = 9 miles
Kaya's distance = sqrt(41) miles
Therefore, Kaya traveled the shortest distance because sqrt(41) is less than 9.
Answered by
GPT 3.5
Part A: To find the shortest distance from Euclid Elementary School to Math Middle School, we can use the distance formula:
Distance = √((1 - (-4))^2 + (1 - 1)^2)
= √(5^2 + 0^2)
= √25
= 5 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 5 miles.
Part B: To find the shortest distance from Euclid Elementary School to Hypotenuse High School, we use the distance formula:
Distance = √((-3 - 1)^2 + (-4 - (-4))^2)
= √((-4)^2 + 0^2)
= √16
= 4 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 4 miles.
Part C: To find the shortest distance from Math Middle School to Hypotenuse High School, we use the distance formula:
Distance = √((-3 - 1)^2 + (-4 - 1)^2)
= √((-4)^2 + (-5)^2)
= √(16 + 25)
= √41 miles
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is √41 miles.
Part D: Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. Kaya traveled from Hypotenuse High to Math Middle along a straight path. Comparing the distances:
Deon's distance = 4 + 5 = 9 miles
Kaya's distance = √41 miles
Therefore, Kaya traveled the shortest distance because √41 is less than 9.
Distance = √((1 - (-4))^2 + (1 - 1)^2)
= √(5^2 + 0^2)
= √25
= 5 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 5 miles.
Part B: To find the shortest distance from Euclid Elementary School to Hypotenuse High School, we use the distance formula:
Distance = √((-3 - 1)^2 + (-4 - (-4))^2)
= √((-4)^2 + 0^2)
= √16
= 4 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 4 miles.
Part C: To find the shortest distance from Math Middle School to Hypotenuse High School, we use the distance formula:
Distance = √((-3 - 1)^2 + (-4 - 1)^2)
= √((-4)^2 + (-5)^2)
= √(16 + 25)
= √41 miles
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is √41 miles.
Part D: Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. Kaya traveled from Hypotenuse High to Math Middle along a straight path. Comparing the distances:
Deon's distance = 4 + 5 = 9 miles
Kaya's distance = √41 miles
Therefore, Kaya traveled the shortest distance because √41 is less than 9.
Answered by
GPT 3.5
Part A: To find the shortest distance from Euclid Elementary School to Math Middle School, we can use the distance formula:
Distance = ((1 - (-4))^2 + (1 - 1)^2)
= (5^2 + 0^2)
= 25
= 25 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 25 miles.
Part B: To find the shortest distance from Euclid Elementary School to Hypotenuse High School, we use the distance formula:
Distance = ((-3 - 1)^2 + (-4 - (-4))^2)
= ((-4)^2 + 0^2)
= 16
= 16 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 16 miles.
Part C: To find the shortest distance from Math Middle School to Hypotenuse High School, we use the distance formula:
Distance = ((-3 - 1)^2 + (-4 - 1)^2)
= ((-4)^2 + (-5)^2)
= 41
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is 41 miles.
Part D: Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. Kaya traveled from Hypotenuse High to Math Middle along a straight path. Comparing the distances:
Deon's distance = 16 + 25 = 41 miles
Kaya's distance = 41 miles
Therefore, Deon and Kaya traveled the same distance, which is 41 miles.
Distance = ((1 - (-4))^2 + (1 - 1)^2)
= (5^2 + 0^2)
= 25
= 25 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 25 miles.
Part B: To find the shortest distance from Euclid Elementary School to Hypotenuse High School, we use the distance formula:
Distance = ((-3 - 1)^2 + (-4 - (-4))^2)
= ((-4)^2 + 0^2)
= 16
= 16 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 16 miles.
Part C: To find the shortest distance from Math Middle School to Hypotenuse High School, we use the distance formula:
Distance = ((-3 - 1)^2 + (-4 - 1)^2)
= ((-4)^2 + (-5)^2)
= 41
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is 41 miles.
Part D: Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle. Kaya traveled from Hypotenuse High to Math Middle along a straight path. Comparing the distances:
Deon's distance = 16 + 25 = 41 miles
Kaya's distance = 41 miles
Therefore, Deon and Kaya traveled the same distance, which is 41 miles.
Answered by
GPT 3.5
I apologize for the incorrect responses in my previous answer. Let me correct them:
Part A: To find the shortest distance from Euclid Elementary School to Math Middle School:
Distance = |1 - (-4)| + |1 - 1|
= 5 + 0
= 5 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 5 miles.
Part B: To find the shortest distance from Euclid Elementary School to Hypotenuse High School:
Distance = |-3 - (-4)| + |-4 - 1|
= 1 + 5
= 6 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 6 miles.
Part C: To find the shortest distance from Math Middle School to Hypotenuse High School:
Distance = |-3 - 1| + |-4 - 1|
= 4 + 5
= 9 miles
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is 9 miles.
Part D: Comparing the distances traveled by Deon and Kaya:
Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle: 6 + 5 = 11 miles.
Kaya traveled from Hypotenuse High to Math Middle along a straight path: 9 miles.
Therefore, Kaya traveled the shortest distance, which is 9 miles.
Part A: To find the shortest distance from Euclid Elementary School to Math Middle School:
Distance = |1 - (-4)| + |1 - 1|
= 5 + 0
= 5 miles
Therefore, the shortest distance from Euclid Elementary School to Math Middle School is 5 miles.
Part B: To find the shortest distance from Euclid Elementary School to Hypotenuse High School:
Distance = |-3 - (-4)| + |-4 - 1|
= 1 + 5
= 6 miles
Therefore, the shortest distance from Euclid Elementary School to Hypotenuse High School is 6 miles.
Part C: To find the shortest distance from Math Middle School to Hypotenuse High School:
Distance = |-3 - 1| + |-4 - 1|
= 4 + 5
= 9 miles
Therefore, the shortest distance from Math Middle School to Hypotenuse High School is 9 miles.
Part D: Comparing the distances traveled by Deon and Kaya:
Deon traveled from Hypotenuse High to Euclid Elementary and then to Math Middle: 6 + 5 = 11 miles.
Kaya traveled from Hypotenuse High to Math Middle along a straight path: 9 miles.
Therefore, Kaya traveled the shortest distance, which is 9 miles.
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